The blustery conditions at Bramall Lane made things tough for both teams and there were few clear-cut chances in the game.
Former Blade Dominic Calvert-Lewin went close just before the half-hour mark. The striker, with 11 Premier League goals this season, chested Michael Keane’s pass past Jack Robinson before unleashing a fierce volley narrowly wide.
The Blades’ best chance of the first half saw David McGoldrick round goalkeeper Jordan Pickford before his shot was cleared from just in front of the goal line by Godfrey.
The hosts thought they should have had a penalty early in the second half when half-time substitute Oli McBurnie went down after tussling with Keane. There was definitely a slight push by the Everton defender but VAR decided that it was not enough to award a penalty.
Everton had been knocking on the door and made the breakthrough with 10 minutes remaining when Sigurdsson scored to give them the lead, beating Ramsdale with a low shot following some good build-up play involving Abdoulaye Doucoure and Bernard.
Wilder’s side threw all they had at Everton in the closing stages but the visitors seemed confident backing themselves to see out the game with 10 men behind the ball.
Chris Wilder’s side have lost 13 of their 15 Premier League matches and are only the third club in top-flight history to be without a win on Boxing Day, after Burnley in 1889-90 and Bolton in 1902-03.